Given this pair of slopes, what is the value of n if the lines are parallel? What is the value of n if the lines are perpendicular?


\({3 \over n}\),\(-{7 \over 2}\)


If I cross multiply, the parallel slope is \(n = -{6 \over 7}\), is that right?

As for perpendicular... how would I solve for that?

 Apr 8, 2018

Parallel lines have the same slope.


If the lines are parallel, then the slopes of the lines are equal.


If the lines area parallel, then....


\(\frac3n\,=\,-\frac72 \\~\\ 3\cdot2\,=\,-7\cdot n \\~\\ 6\,=\,-7n\\~\\ n\,=\,-\frac67\)


....You're right!!! laugh


If the lines are perpendicular, then the slopes are negative reciprocals of each other.


That means   \(\frac3n\)   must equal the negative reciprocal of   \(-\frac72\)  .


The negative reciprocal of   \(-\frac72\)   is    \(\frac27\)  .


If the lines are perpendicular, then....


\(\frac3n\,=\,\frac27\\~\\ 7\cdot3\,=\,2\cdot n\\~\\ 21\,=\,2n\\~\\ n\,=\,\frac{21}{2}\)

 Apr 8, 2018

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